Equipartition of the entanglement entropy

The entanglement in a quantum system that possesses an internal symmetry, characterized by the S-z magnetization or U(1) charge, is distributed among different sectors. The aim of this Rapid Communication is to gain a deeper understanding of the contribution to the entanglement entropy in each of those sectors for the ground state of conformal invariant critical one-dimensional systems. Surprisingly, we find that the entanglement entropy is equally distributed among the different magnetization sectors. Its value is given by the standard area law violating logarithmic term that depends on the central charge c, minus a double logarithmic correction related to the zero-temperature susceptibility. This result provides a method to estimate simultaneously the central charge c and the critical exponents of U (1)-symmetric quantum chains. The method is numerically simple and gives precise results for the spin 1/2 quantum XXZ chain. We also compute the probability distribution of the magnetization in contiguous sublattices.